The goal of this section is to show that the statistical solutions of Navier–Stokes as introduced by Foiaş and Prodi [1]}, [2]}, [3]}, [4]}, [5]} are equivalent to families of correlation measures as introduced in [6]} that satisfy the Friedman–Keller system of moment equations. For the sake of simplicity we will assume that the support of the initial measure \(\mu _0\)  lies in a bounded set \(B\subset L^2(D;U)\) , that is,
\(\text{supp}(\mu _0)\subset B\subset L^2(D;U).\) 
